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I believe this is right but double check to make sure :)
The statement about pointwise convergence follows because C is a complete metric space. If fn → f uniformly on S, then |fn(z) − fm(z)| ≤ |fn(z) − f(z)| + |f(z) − fm(z)|, hence {fn} is uniformly Cauchy. Conversely, if {fn} is uniformly Cauchy, it is pointwise Cauchy and therefore converges pointwise to a limit function f. If |fn(z)−fm(z)| ≤ ε for all n,m ≥ N and all z ∈ S, let m → ∞ to show that |fn(z)−f(z)|≤εforn≥N andallz∈S. Thusfn →f uniformlyonS.
2. This is immediate from (2.2.7).
3. We have f′(x) = (2/x3)e−1/x2 for x ̸= 0, and f′(0) = limh→0(1/h)e−1/h2 = 0. Since f(n)(x) is of the form pn(1/x)e−1/x2 for x ̸= 0, where pn is a polynomial, an induction argument shows that f(n)(0) = 0 for all n. If g is analytic on D(0,r) and g = f on (−r,r), then by (2.2.16), g(z) =
When minerals are exposed to high pressure and temperatures, the individual minerals begin to realign themselves
Answer:
<em>The bullet was 0.52 seconds in the air.</em>
Explanation:
<u>Horizontal Motion
</u>
It occurs when an object is thrown horizontally with a speed v from a height h.
The object describes a curved path ruled exclusively by gravity until it hits the ground.
To calculate the time the object takes to hit the ground, we use the following equation:
Note it doesn't depend on the initial velocity but on the height.
The bullet is fired horizontally at h=1.3 m, thus:
t = 0.52 s
The bullet was 0.52 seconds in the air.
